SOLUTION: 1. Show that the sum of any two odd numbers is always an even number. 2. Show that the product of any two even numbers is divisible by four.

Algebra ->  Sequences-and-series -> SOLUTION: 1. Show that the sum of any two odd numbers is always an even number. 2. Show that the product of any two even numbers is divisible by four.      Log On


   

Question 380584: 1. Show that the sum of any two odd numbers is always an even number.
2. Show that the product of any two even numbers is divisible by four.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

1) An even number is any integer divisible by 2. 

Let 2n +1  and 2k + 1 represent two odd numbers

 (2n + 1) + (2k + 1) = 2(n+k+1) 

Letting N = (n+k+1)

 2n + 1 + 2k + 1 = 2N  sum is an even number as the integer is divisible by 2

Resulting Number is a number divisible by 2, therefore even

2) Let 2n  and 2k represent two even numbers

  2n*2k = 4(nk) Resulting Number is divisible by 4